Multiplication rules are very similar. Again we imagine that the reader
knows how to multiply real numbers (using a calculator, even) so that
the idea of multiplication of numbers as a *process* is familiar.
In that case, the reader can easily verify for themselves that given
real numbers , , , the following are all true. They are true
for *complex* , , and as well (trust me), but that's a lot
easier to show *after* we've worked out the rules for real numbers,
in particular distributivity. We have to work a bit harder on inversion
and division, as well.

(3.16) | |||

(3.17) | |||

(3.18) | |||

(3.19) |

Once again we see that for expressions that contain only multiplied terms
we can group them in any order:

(3.20) |

There are more rules

In physics one *can* multiply symbols with different units, such an
equation with (net) units of meters times symbols given in seconds. In
the end, however, the units on both sides must be consistent and make
sense.